President Carter, declaring that the foundations of international law and institutions are threatened by the Iranian crisis, announced yesterday that the United States will ask the United Nations Security Council next week to impose economic sanctions against Iran.

In a grim statement to reporters before he left Washington to spend the Christmas holidays at Camp David, Md., Carter said it is clear that if there is to be a peaceful resolution of the crisis, "concrete action must be taken by the international community."

He accused Iranian authorities of standing "in arrogant defiance of the world community" by refusing to release the American hostages, who have been held since Nov. 4, and said the U.N.'s credibility will be judged by the outcome of the Security Council debate.

"The Security Council must act to enforce its demand that Iran release the hostages," the president said. "The world community must support the legal machinery it has established, so that the United Nations and the International Court of Justice will continue to be relevant in settling serious disputes which threaten peace among nations."

The prospects for Security Council adoption of economic sanctions, even in diluted form, were certain. Nine affirmative votes must be obtained from the 15-member council, and none of the five permanent members, which include the Soviet Union and China, must cast a veto.

The Soviet position is unclear, despite advance soundings by Secretary of State Cyrus R. Vance. The Soviets have opposed the taking of hostages, even while attacking U.S. policies in Iran and seeking to win a future position of strength in the gathering chaos there.

Briefed by the president just before his announcement, senior Democratic and Republican senators said the Soviet stand on sanctions would have a major effect of Senate approval of the pending strategic arms limitation treaty (SALT II). Senate Foreign Relations Committee Chairman Frank Church (D-Idaho) said a Soviet veto would be "a very hostile act" that would have "serious and adverse consequences."

China, whose representative currently serves as chairman of the Security Council, is expected to abstain in view of its own efforts to win favor in Iran.

The key to a successful outcome is the posture of the nonaligned countries of the Third World, especially influential African states, according to head-counters in New York. Among the current council members, Nigeria and Zambia are expected to be particularly important. Other nonaligned nations whose votes are in doubt are Bangladesh, Bolivia, Gabon, Jamaica and Kuwait.

African delegates have expressed irritation and some bitterness at being asked to support U.S. sponsored economic sanctions against Iran, in view of Washington's longstanding objections to -- and vetoes of -- black African demands for sweeping economic and military sanctions against South Africa. Arab delegates, who discussed the U.S. move in a meeting yesterday, were caustic about past American failure to agree to sanctions against Israel.

The hope of American officials is to make the case that the issue of diplomatic hostage-taking is different from others in degree as well as substance. After Third World delegates vent their criticisms of the United States in corridor talks and speeches, they will have to face the more difficult problem of an actual vote with Americans and the world looking on.

Sen. Jacob Javits (R-N.Y.) said after the White House briefing that support of other countries is "a big-ticket item for us." He said members of the Security Council should understand that "the American people are going to measure our friendship on the backing we get at the United Nations."

U.S. officials expressed assurance about five votes in support of a sanctions resolution -- from Britain, France, Norway and Portugal in addition to the United States' own vote.

The makeup of one-third of the Security Council will change Jan. 1 and several Third World countries will be replaced by other Third World nations with somewhat closer ties to Washington. But the current expectation is that the vote on the U.S. sanctions plan will come before the end of the year, probably next week.

State Department officials said that for now, on humanitarian grounds, the United States will not seek to stop the flow of food and drugs to Iran, although an official pointedly suggested that a ban on the shipment of these items to Iran might be sought if the crisis continues.

Officials also said the United States is not seeking to affect the export of Iranian oil to Europe, Japan and other nations through the U.N. sanctions, which would be limited to Iranian imports.

Beyond this, the details of what the United States is seeking were left unclear and subject to negotiation with other Security Council members. However, a State Department official emphasized that the United States is seeking "meaningful," rather than symbolic, action.

Article 41 of Chapter VII of the U.N. Charter, which will be cited in Washington's effort, authorizes the Security Council to impose an extensive list of measures against violators of U.N. decisions. The list includes "complete or partial interruption of economic relations and of rail, sea, air, postal, telegraphic, radio and other means of communication, and the severance of diplomatic relations."

For practical reasons and in order to win nine Security Council votes the U.S. demand is likely to fall well short of the entire list.

There is no assurance that a Security Council vote to impose economic sanctions would be totally effective in shutting off the flow of the items listed, nor is there assurance that the hostages would be released even if it is highly effective.

American officials spoke of the sanctions request as the next step in the deliberate and measured program of pursuing all available means short of military force to show U.S. earnestness and good faith, while mobilizing the community of nations behind the demand that the hostages be released.

At the same time, officials maintained that the Iranian economy has been increasingly squeezed. "The country is in serious economic difficulty already," said an official who anticipated that sanctions would make Iran's problems far greater than they are now.

State Department spokesman Hodding Carter said the aim of the U.S. program of economic restriction is "to produce a change in attitude among those who control Iran and thus the hostages." He said the United States assumes that the external pressures eventually will cause the Iranian authorities to listen to reason.

In a related action, the U.S. Export-Import Bank yesterday declared in default more than $245 million in loans to Iran. The action will shut off further U.S. export credits to Iran, place the United States in a position to attach Iranian assets to cover losses and enable Washington to negotiate with similar banks around the world to urge parallel action.

The president's statement at the White House, which was broadcast live by the three commercial television networks, contained the implicit threat of eventual U.S. military action that the administration has previously invoked. The president noted the United States' desire for a peaceful solution to the crisis, which he said would be preferable "to the other remedies which are available to us under international law."

Carter also used harsh language in referring to the ruling Iranian authorities, who he said have "shown contempt, not only for international law, but for the entire international structure for securing the peaceful resolution of differences among nations."

"In an irresponsible attempt at blackmail, to which the United States will never yield, kidnappers and terrorists supported by Iranian officials continue to hold our people under inhumane conditions," he said.

The carefully prepared statement also noted that the crisis represents a test of the U.N.'s ability to enforce its call for release of the hostages, an argument American representatives undoubtedly will make during the Security Council debate over imposing sanctions.

"I think of no more clear and complelling challenge to the international community than the one we face today," the president said. "The lives of over 50 innocent people are at stake. The foundation of civilized diplomacy is at stake. The integrity of international law is at stake. The credibility of the United Nations is at stake."

Carter added, in a second reference to the possibility of military action: "And at stake ultimately is the maintenance of peace in the region."

The Iranian Foreign Ministry withheld comment early today on Carter's appeal for U.N. sanctions. A spokesman said the ruling Revolutionary Council would have to consider the president's statement, the Associated Press reported.

Iran's leader, Ayatollah Ruhollah Khomeini, had anticipated Carter's action. A few hours before the president's speech, Khomeini told a group of revolutionary guards that Iran would defy any sanctions.

He was quoted by the government radio as saying that if sanctions were imposed, Iran would ask "other countries to meet our economic requirements."

The broadcast reported that Khomeini said a number of nations, which he did not name, were swinging to Iran's side in the crisis. "Other governments are not America's subordinates," he was quoted as saying.

In another development, the nuclear aircraft carrier Nimitz is being sent to the Gulf of Oman to replace the carrier Kitty Hawk, defense officials said last night. The U.S. Navy now has 21 ships in the area. The Nimitz, accompanied by two nuclear-powered cruisers, is expected to arrive late next month after a trip around the Cape of Good Hope.